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Trigonometry of a right triangle

Source: Czech and Slovak Olympiad 1973, National Round, Problem 1

July 16, 2024
trigonometryright trianglegeometry

Problem Statement

Consider a triangle such that sin⁡2α+sin⁡2β+sin⁡2γ=2.\sin^2\alpha+\sin^2\beta+\sin^2\gamma=2. Show that the triangle is right.
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